I’ve tried to find a little try to find happiness even fromin trivial things.

For example, I could sleep a little longer this morning because of a business trip, so I happily ate breakfast and made an espresso.

There are always not greatbad things each day, so I need to make myself happy somehow.

For example, I could sleep a little longer this morning because of a business trip, so I happily ate breakfast and made espresso.

There are always things that are not great things each day, so I need to make myself happy somehow.

more natural phrasing, "not" in an adjective position is something that happens in very casual speech, but it's not considered correct.

For example, I could sleep a little longer this morning because of a business trip, so I happily ate breakfast and made espresso.

I’ve tried to find a little happiness even from trivial things.

If you want to say that you regularly make an effort to find happiness from trivial things, you would say "I try to find..."

For example, I could sleep a little longer this morning because of a business trip, so I happily ate breakfast and made espresso.

There are always not great things each day, so I need to make myself happy somehow.

I don't think this is a grammatical thing, so I didn't correct it, but we generally don't use negated adjectives to modify a noun directly. Here are some ways to fix it:
Use a different adjective: "There are always bad things each day."
Modify "always" instead: "There are not always great things each day."
Not that these have slightly different meanings.